How do I attach rope to a mesh
You can use an empty and hooks.

Select the sail, enter edit mode and select the vertex at end of the rope that should be attached to the rope, then press Ctrl+H and select Hook to new object. An empty will be created at the same position of the vertex, so that if that if the vertex moves it will make the empty follow the movement



Exit edit mode and select the newly created empty. Press Shift+S and select cursor to selected. This will place the 3D cursor where the empty is.

With the Empty still selected, press Shift select the rope. This will make the rope the Active object but keeping the empty selected as well

To align the end of the rope at the edge of the sail, enter Edit mode, select the control point that should be controlled by the empty, press Shift+S and this time select selection to cursor, so that the end of the rope ends at the same place as the empty.



The next step is to parent the control point of the curve to the empty, to do that press Ctrl+P and select "Make Vertex Parent". This will make the control point be pinned to the empty, and in turn, be pinned to the vertex on the sail.

Now if you move the control point of the vertex it will move the empty and the empty in turn will move the sail. If the rest of the sail moves, the pinned vertex will remain in place.



Edit:

For this example the sail is a simple quad (just 4 vertices) with a subsurf modifier set to Simple. 

Read also:
How to simulate a rope?